Research on the Discovery of Timing Causal Structure in Epidemic

Prevention and Control

Tengjiao Mao, Chunxiao Cai, Yue Lu

, Ruihua Wang and Wei Liu

Center for Strategic Assessment and Consulting, AMS, Beijing 100097, China

∗

Corresponding author

Keywords: Epidemic Prevention and Control, Timing Causation, Dimensionality Reduction, Convergence.

Abstract: Decision-makers need to timely and accurately identify departments with unfavorable handling based on the

effect of epidemic prevention and control, which requires the construction of a timing causal structure between

departments. In consideration of a large number of departments and influencing factors involved, traditional

algorithms are more costly to construct causal structures. In this paper, the departments involved in epidemic

prevention and control and related factors are analyzed. A causality analysis framework based on Bayesian

networks is proposed. The dimensionality of data is reduced based on time-varying characteristics. Bayesian

network structure learning algorithms are used to build a structural model based on timing causality. The

results of the simulation case show that the method takes the advantage of fast convergence and accurate

causality.

1 INTRODUCTION

Inferring causal relationships between things is a hot

topic in the study of data relationships. Causal infer-

ence methods, as the main means of causality re-

search, have been widely used in the fields of policy

evaluation, fault diagnosis, biomedicine, etc. For ex-

ample, researchers have applied causal inference

models in disease diagnosis, biological network infer-

ence, and drug efficacy analysis in the biomedical

field (Sesia, 2020; Shen, 2020; Zhou, 2010; Dong,

2014; Cai, 2013; Liu, 2014). In the field of communi-

cation and industry, some scholars have applied

Bayesian networks to fault diagnosis and perfor-

mance optimization studies of networks (Hao, 2016;

Trave-Massuyes, 1997; Hu, 2013). In the field of so-

cial networks, researchers have tried to use causal dis-

covery models to study the causal relationships of

user behaviors (Ver Steeg, 2012; Duan, 2013; Sun,

2014; Sun, 2015).

Exploring the causal relationship between various

departments in epidemic prevention and control is

also needed. Especially in the case of poor prevention

and control, a higher degree of accuracy and timeli-

ness is required to trace the problem and allocate re-

sponsibility, so that the relevant departments can be

targeted to rectify and effectively curb the spread of

the epidemic on time. Therefore, it is relevant to re-

search the discovery method of the causal structure of

departments in epidemic prevention and control

based on timing multidimensional data.

The widely used causal inference methods are

mainly divided into Rubin's potential outcome model

and Pearl's SCM (structure causal model). Causal

structure discovery methods mainly rely on causal

structure learning models, which are mainly classified

as conditional independence constraint-based meth-

ods (Pearl, 2009; Le, 2016; Cai, 2011; Tu, 2019) and

scoring-based methods (Ramsey, 2017; Huang, 2018;

Zheng, 2018). Conditional independence constraint-

based methods learn the causal structure by judging

the independence and conditional independence in-

formation between nodes, and typical algorithms are

the PC (Peter-Clark) algorithm and IC (Inductive

Causation) algorithm. Scoring-based methods dis-

cover causal structures by scoring them based on ob-

served data, typical methods are GES (Greedy equiv-

alence search) and FGES (fast greedy equivalence

search).

However, there are many departments and emer-

gencies involved in epidemic prevention and control,

and the factors that affect the handling capabilities of

departments result in large changes in the timing epi-

demic prevention results. To accurately learn the

causal structure among departments, a great amount.

386

Mao, T., Cai, C., Lu, Y., Wang, R. and Liu, W.

Research on the Discovery of Timing Causal Structure in Epidemic Prevention and Control.

DOI: 10.5220/0011737900003607

In Proceedings of the 1st International Conference on Public Management, Digital Economy and Internet Technology (ICPDI 2022), pages 386-392

ISBN: 978-989-758-620-0

 2023 by SCITEPRESS – Science and Technology Publications, Lda. Under CC license (CC BY-NC-ND 4.0)

Figure 1: Diagram of epidemic prevention and control based on timing changes.

of multi-dimensional timing sample data is required.

The learning cost is too high if traditional algorithms

are used directly. To solve the above problems, the

key elements in epidemic prevention and control are

analyzed and summarized. The dimensionality of the

data is reduced based on the timing change character-

istics. Timing causal structures are constructed

through scoring-based learning algorithms. Finally,

simulated data are utilized to verify the effectiveness

of the algorithm. The simulation results indicate that

the proposed algorithm can effectively reduce the di-

mensionality of data, which results in faster conver-

gence speed and lower learning costs

2 CONSTRUCTION OF

MULTI-DIMENSIONAL

TIMING NODE CAUSAL

STRUCTURE DISCOVERY

MODEL

2.1 Analysis of Key Departments and

Influencing Factors

A city's emergency plan for epidemic prevention and

control is taken as an example in the paper (Shanghai

municipal health commission, 2020). The depart-

ments mainly involved in epidemic prevention and

control include the Health Commission, the publicity

departments, the grassroots communities, hospitals,

and the disease control departments. Their main func-

tions in epidemic prevention and control are summa-

rized as follows.

The Health Commission is responsible for formu-

lating disease prevention plans and immunization

plans, and implementing intervention measures for

public health problems which endanger people’s

health.

The publicity department is responsible for publi-

cizing epidemic prevention policies, monitoring and

controlling online public opinion, etc.

The hospital is responsible for treating patients

and assisting in disease testing and virus elimination.

The disease control department is responsible for

epidemiological investigation of cases, case closure

and virus elimination efforts.

The grassroots community is responsible for mon-

itoring the health of people in the community, regu-

larly organizing disease screenings, and conducting

preliminary disposition, reporting, and prevention

and control once cases are detected.

Research on the Discovery of Timing Causal Structure in Epidemic Prevention and Control

387

The departments above all play an important role

in epidemic prevention and control. When emergen-

cies come, each department needs to handle the situ-

ation individually or collaboratively. There are also

many factors that affect the handling ability of depart-

ments, including operational capability, epidemic

handling attitude, epidemic handling quantity, epi-

demic disposal time, and severity of the epidemic.

With the change of time and the influence of various

factors, the handling capacity of each department will

not always remain the same. Changes in handling ca-

pacity will affect the result of epidemic prevention

and control, as shown in Fig.1.

Because of the great number of departments and

factors involved and the timing change, it is necessary

to construct a causal structure to timely discover the

influence relationship among departments.

2.2 Algorithm Model Construction

In Pearl's structural causal model (Pearl, 2009), a

DAG (directed acyclic graph) is used to construct the

causal structure. In this paper, departments and pre-

vention results are used as variable nodes.

Take the simplest case as an example. The han-

dling capacity of departments is influenced by the

above five factors., and it is assumed that each factor

has only two states which are denoted as 0 and 1 re-

spectively at moment

. The state of the node repre-

sented by each department at that moment has

possible values which are noted as binary from 00000

to 11111. As an outcome node, the epidemic preven-

tion result is usually measured by the number of in-

fected people at moment

Each node takes 5 factors into consideration, re-

sulting in an excessive number of possible values. It

will greatly reduce the efficiency of the structure

learning algorithm if the causal structure is learned in

this way. It is necessary to improve the model and re-

duce the dimensionality of the data. The specific di-

mensionality reduction method is as follows.

In the original data, a 5-bit binary number is taken

to represent the value of the node state. The state of

each node at different times is counted, and the state

of nodes at two adjacent moments is compared. If the

value of node state remains unchanged, it is recorded

as 0, and if the value of node state changes, it is rec-

orded as 1. Therefore, 1-bit binary number can be

used to represent the state changes of department

nodes in the adjacent periods, so as to realize the di-

mension reduction of the number of department node

values, as is shown in Fig.2. Considering the changes

in epidemic prevention results, when the number of

infected people increases, it can be considered that the

prevention results have become worse (recorded as -

1); when the number of infected people falls, the pre-

vention results can be considered better (recorded as

1); when the number of infected people remains un-

changed, the prevention results can be considered un-

changed (recorded as 0).

As time advances, multiple sets of data on node

state changes will be formed. Finally, according to the

dimensionality-reduced data, the corresponding

causal graph is derived with a score-based Bayesian

structure learning algorithm.

3 SIMULATION VERIFICATION

To verify the validity of the model in this paper, the

causal structure between departments is preset in the

context of epidemic prevention and control in a city,

and the timing change data is generated according to

this structure. Based on the generated data, the tradi-

tional learning algorithm and proposed algorithm are

utilized to learn the causal structure separately, and

the learning results and costs are compared and ana-

lyzed to verify the validity of the algorithm.

Figure 2: Diagram of node value dimensionality reduction.

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388

The simulation flow is shown in Fig.3.

Figure 3: The diagram of simulation flow.

Figure 4: summarized causal structure.

3.1 Data Generation and

Dimensionality Reduction

According to the contents of the emergency manage-

ment plan and work measures for municipal epidemic

prevention and control (Shanghai municipal health

commission, 2020), the influence relationship be-

tween departments and the epidemic prevention result

is qualitatively summarized as shown in Fig.4.

Different moments are divided evenly in enough

time. At each moment, the state of each node is gen-

erated with a certain conditional probability accord-

ing to the influence relationship in Fig.4. In this way,

the state value (5-bit) of each node is generated as

sample data. Assuming that the sample data at each

moment belongs to independent and identical distri-

bution, multiple sets of simulated data are generated

in this way. Traditional algorithms perform causal

structure learning based on this data.

Research on the Discovery of Timing Causal Structure in Epidemic Prevention and Control

389

The dimensionality of the simulated data is re-

duced with the proposed algorithm. And multiple sets

of node state change data (1-bit) for different time pe-

riods are formed. The proposed algorithm learns the

causal structure based on the data.

3.2 Criteria For Comparison of Results

In order to measure the difference between the pro-

posed algorithm which learns after dimensionality re-

duction and the traditional algorithm, the results are

compared and analyzed in terms of learning effect

and learning cost.

The learning cost is measured by the size of sam-

ples and the time used for learning. The sample size

plays an important role in the result of causal structure

learning, and the accurate structure always cannot be

obtained with little data. Theoretically, the more sam-

ple data is learned, the more accurate the learned

causal structure will be. When a certain amount of

sample data is exceeded, the learned causal structure

will not change. It can be considered that the algo-

rithm has converged and learning has completed. The

size of samples and the learning time is used as the

learning cost when the algorithm converges.

When the algorithm has converged, the effect of

learning is measured by the similarity between the

learned causal structure and the actual causal struc-

ture. If the structure in Fig.4 is assumed to be the ac-

tual causal structure, comparing the causal structure

at the time of algorithm convergence with the causal

structure in Fig.4, it can be concluded that a higher

degree of similarity represents a more accurate

learned causal structure. In order to quantify the de-

gree of similarity between two causal structures, the

concept of Structural Relevance is defined.

Structural Relevance

(Adler, 2010): Struc-

tural Relevance quantitatively characterizes the de-

gree of similarity between two causal structures. The

causal structure can be transformed into the form of a

matrix. If there are

nodes in the causal structure,

it can be represented by a

×nn

matrix. When node

in the causal structure has an arrow pointing to the

node

(node

is the cause of node

), the

value

()

in the corresponding matrix is 1, other-

wise, it is 0. Taking the actual causal structure as an

example, the schematic diagram of its causal structure

transformed into a matrix is shown in Fig.5. Then, the

degree of similarity of two causal structures can be

expressed in terms of the similarity of two matrices.

The matrix transformed by the actual causal structure

is denoted as

, and the matrix transformed by the

matrix obtained from learning is denoted as

. The

specific formula for the structural correlation

as follows.

()

−−



−−







 

nn nn

AABB

AA BB

(or

) is equivalent to averaging the value of

all elements in

(or

), and

is the matrix

rank. The closer the value

is to 1, the more simi-

lar the two structures are meant to be. When

, it

indicates that the actual causal structure is learned.

Figure 5: Schematic diagram of the actual causal structure

transformation matrix.

3.3 Results Display and Analysis

With the traditional algorithm and the proposed algo-

rithm in this paper, the correct causal structure ob-

tained after the final algorithm convergence is shown

in Fig.6.

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390

Figure 6:Learned causal structure.

The convergence of the algorithm is shown in Fig.7.

Figure 7: The diagram of algorithm convergence.

Both methods learned the actual causal structure

from Fig.6. But there are significant differences in

learning cost. According to Fig.7, 800000 samples are

required for the traditional algorithm to learn the ac-

tual causal structure. While for the proposed algo-

rithm, only 800 samples are needed to learn the actual

causal structure. The size of samples learned by this

algorithm is reduced by 1000 times. From the per-

spective of learning time, the convergence time of the

traditional algorithm is 11250s, while the conver-

gence time of the proposed algorithm is 10s. The time

cost is reduced by 1125 times.

It can be seen that the proposed algorithm learns

an accurate causal structure based on the simulated

data, and greatly outperforms the traditional algo-

rithm in terms of time cost and the size of samples,

which verifies the advantages and effectiveness of the

proposed algorithm. When using real data, this

method is equally applicable and advantageous.

4 CONCLUSION

In order to construct an accurate causal structure and

reduce the cost of learning, the dimension of timing

data is reduced based on the changing features and the

causal structure is constructed through the structural

learning algorithms in this paper. The proposed algo-

rithm and the traditional algorithm are compared in

learning effect and cost with an example. The pro-

posed algorithm takes the advantage of fast conver-

gence and accurate causality. However, the size of

samples required by the proposed algorithm is still

considerable in actual needs, so the size of samples

required for learning needs to be further reduced in

the next research to achieve better results.

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